In the seminar, we will cover the basics of the theory of abelian varieties (i.e., proper varieties over a field with a group structure). Abelian varieties of dimension 1 are the same as elliptic curves. Studying these subjects will allow us at the same time to practice working with schemes and applying the results of the algebraic geometry courses. If there is enough time at the end, we might look at parameter spaces (so called moduli spaces) for abelian varieties.

Prerequisites: Algebraic Geometry 1. If you have not yet attended an Algebraic Geometry 2 class, you should take the one offered in parallel: Algebraic Geometry 2

Date and time: Tue, 2:00 – 3:30pm, S-U-3.03, first meeting: April 16.

Contact: ulrich.goertz@uni-due.de

Seminar program: pdf

Organizational meeting: Wed, April 3, 2:15pm, S-3.14. You can also decide for a talk before the meeting — just send me an email.

Talks

1 Introduction Ulrich Görtz April 16
2 Group schemes Ahmed Elashry April 23
3 Abelian varieties: definition and first properties Gregor Kremers May 14
4 Coherence of higher direct images under proper morphisms Ulrich Görtz May 21
5 Cohomology and base change I Marc Kohlhaw May 28
6 Cohomology and base change II Heer Zhao June 4
7 The theorem of the cube Xucheng Zhang June 18
8 Applications of the theorem of the cube I Yusuff Ogundipe June 25
9 Applications of the theorem of the cube II Yusuff Ogundipe July 2
10 Elliptic curves Jan Wulf July 9